Section 1.5 Homework

1.   What does it mean when a part of the population is​ under-represented? Choose the correct answer below.

1. A part of the population is​ under-represented when it is proportionally smaller in its population than in a sample.
2. A part of the population is​ under-represented when their answers on a survey tend not to reflect their true feelings.
3. A part of the population is​ under-represented when individuals selected to be in the sample who do not respond to the survey have different opinions from those who do.
4. A part of the population is​ under-represented when it is proportionally smaller in a sample than in its population.

2.   Distinguish between nonsampling error and sampling error. Choose the correct answer below.

1. Nonsampling error is the error that results from randomness. Sampling error is the error that results from using a sample to estimate information about a population.
2. Nonsampling error is the error that results from​ undercoverage, nonresponse​ bias, response​ bias, or​ data-entry errors. Sampling error is the error that results because a sample is being used to estimate information about a population.
3. Nonsampling error is the error that results because a sample is being used to estimate information about a population. Sampling error is the error that results from​ undercoverage, nonresponse​ bias, response​ bias, or​ data-entry errors.
4. Nonsampling error is the error that results from the process of obtaining the data. Sampling error is the error that results from​ undercoverage, nonresponse​ bias, response​ bias, or​ data-entry errors.

3.  The manager of a shopping mall wishes to expand the number of shops available in the food court.  She has a market researcher survey the first 80 customers who come into the food court during weekday afternoons to determine what types of food the shoppers would like to see added to the food court. Complete parts​ (a) and​ (b) below.

​(a) The survey has bias. Determine whether the flaw is due to the sampling method or the survey itself. For biased​ surveys, identify the cause of the error.

What is the cause of the​ bias?

1. Nonresponse
2. Response bias
3. Sampling bias

 ​(b) Suggest a remedy to the problem.

Which of the following is the best way to remedy this​ problem?

1. Increase the sample size so that more people respond to the question.
2. Reword the question so that it is balanced.
3. Ask customers throughout the day on both weekdays and weekends.

4.   The survey has bias.​ (a) Determine the type of bias.​ (b) Suggest a remedy.

A pro-military advocate wants to estimate the percentage of people who favor increasing funding for the military.  He conducts a nationwide survey of 1260 randomly selected adults 18 years and older. The interviewer asks the​ respondents, ​”Do you favor being patriotic by supporting our armed forces?​”

​(a) Which of these best describes the bias in the​ survey?

1. Sampling bias
2. Response bias
3. Undercoverage bias
4. Nonresponse bias

​

(b) How can the bias be​ remedied?

1. The interviewer should survey a greater number of adults 18 and older.
2. The interviewer should survey people under 18 as well.
3. The interviewer should reword the question.
4. The interviewer should survey people by phone and in person.

5.  The survey has bias.​ (a) Determine the type of bias.​ (b) Suggest a remedy.  A polling organization conducts a study to estimate the percentage of households that home school their children. It mails a questionnaire to 1888 randomly selected households across the country and asks the head of each household if he or she home schools their children. Of the 1888 households​ selected, 39 responded.

​(a) Which of these best describes the bias in the​ survey?

1. Response bias
2. Nonresponse bias
3. Sampling bias
4. Undercoverage bias

​(b) How can the bias be​ remedied?

1. The polling organization should mail the questionnaire to each person in the households.
2. The polling organization should only select households in a single state.
3. The polling organization should mail the questionnaire to a greater number of households.
4. The polling organization should try contacting households that do not respond by phone or​ face-to-face.

6.  ”Would you be interested in participating in a short health-related survey? If you qualify and complete this survey, you will receive $2.00.” What tactic is being used to increase the response rate for this​ survey?

Choose the correct answer below.

1. The company is using callbacks.
2. The company is selecting people randomly.
3. The company is using an online survey.
4. The company is using a reward in the form of the $2.00 payment.

7. Consider the following question from a recent poll. Thinking about how the affirmative action issue might affect your vote for major​ offices, would you vote only for a candidate who shares your views on affirmative action or consider a​ candidate’s position on affirmative action as just one of many important​ factors? [rotated]  Why is it important to rotate the two choices presented in the​ question?

Which of the following is​ correct?

1. The choices need to be rotated to minimize nonresponses.
2. The choices need to be rotated to minimize response biases.
3. The choices need to be rotated to minimize interviewer error.
4. The choices need to be rotated to minimize the effect of a poorly worded question.

8.   Suppose a surveyor wants to conduct a phone survey about a new song. She plans to take a simple random sample.​ However, some people are not at home. Do you believe this can affect the ability of the surveyor to obtain accurate polling​ results? If​ so, how?Choose the correct answer below.

1. ​Yes, because it keeps the people who are less informed from introducing bias to the survey.
2. Yes, especially if the people who are not at home have a trait that is not accurately represented by the remaining people in the sample.
3. ​Yes, because it allows the surveyor to better target her intended demographic.
4. ​No, this does not affect the​ surveyor’s ability to obtain accurate polling results.

9.  What are some solutions to​ nonresponse?  Select all that apply.

1. attempt callbacks
2. change wording of questions
3. use convenience sampling
4. use cluster sampling
5. reduce undercoverage
6. reduce interview error
7. use stratified sampling
8. offer rewards and incentives

1. A rectangular piece of metal is 9 in. longer than it is wide. Squares with sides 3 in. long are cut from the four​ corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 76 in.3​?

Choose the correct answer below.

1. (x+3)(x−6)=76
2. x(x+9)=76
3. (x+3)(x−6)(3)=76

2. Find two consecutive integers whose product is 30.

1. −7, −6
2. ​, 6 and −6, −5
3. 5​, 6
4. 6​, 7 and -7, -6

3.  The product of two consecutive even integers is 168.  Find the integers.

The positive integers are

The negative integers are

4. One leg of a right triangle has a length of 7 m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is __m

The length of the hypotenuse is __m

5.  The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 269 in2.

Find the lengths of the sides of the two squares.

A side of the small square is ____ ​in.; a side of the big square is __ in

6. The area of a rectangular wall of a barn is 100 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

width = __ ft

length = __ ft

7.